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    <title>
      Introduction to astorb.dat
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    <h2>
      <center>
        The Asteroid Orbital Elements Database
      </center>
    </h2>
    <p>
      <font size = +1><b> Introduction </b></font>
      astorb.dat is an ASCII file of high-precision osculating orbital
      elements, ephemeris uncertainties, and some additional data for all the
      numbered asteroids and the vast majority of unnumbered asteroids
      (multi-apparition and single-apparition) for which it is possible to
      make reasonably determinate computations. It is currently about
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            4.3
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Mb in size in its compressed form (astorb.dat.gz),
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           15.7
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      Mb in size when decompressed (astorb.dat), and contains
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             58651
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      orbits computed by me (Edward Bowell). Each orbit, based on astrometric
      observations downloaded from the
      <a href="http://cfa-www.harvard.edu/cfa/ps/mpc.html">Minor Planet
      Center, </a>occupies one 266-column record.
<p>
<font size = +1><b> Special Features of astorb.dat</b></font>
There are three primary differences between our database and conventional
asteroid orbit files.
</p>
<p>
First, <b>we update the database daily.</b> Thus, observations in each new
batch of Minor Planet Circulars will be used in new orbits on a monthly basis,
and those in the Minor Planet Electronic Circulars shortly after they are
published. Other changes, such as the addition of orbits resulting from our
own astrometric observations and the computation of current ephemeris
uncertainties, are being made on a quasi-daily basis. Automatic daily updates
commence at 8 hr UT. The updating process is generally completed by 10:00 UT.
On the UT date of full Moon, the updating process is not completed until
14 hr UT or later.
</p>
<p>
Second, <b>all the orbits in a given version of the file have an epoch of
osculation near the present.</b> Consequently, the ephemerides of most
non-Earth-approaching asteroids can be computed to arcsec accuracy or better
within &#177; 50 days of the epoch using a 2-body ephemeris program.
</p>
<p>
Third, <b>current and future ephemeris uncertainties are given.</b> Observers
will readily be able to estimate whether asteroids are likely to be within
their telescopes' fields of view, and they will better be able to prioritize
astrometric targets.
</p>
<p>
      <font size = +1><b> Landmarks</b></font>
For a reverse chronological listing of significant changes to the database,
click <a href="ftp://ftp.lowell.edu/pub/elgb/astorb_landmarks.html">here</a>.
</p>
<p>
<font size = +1><b> Downloading astorb.dat</b></font>
The file may be obtained by the following means:
<ul>
<li>Get a decompressed version (astorb.dat) via ftp by clicking on
<a href= "ftp://ftp.lowell.edu/pub/elgb/astorb.dat.gz">here</a>. The source
(astorb.dat.gz) is compressed but your browser should automatically decompress
it. If this fails, try getting the original, uncompressed version by clicking
<a href= "ftp://ftp.lowell.edu/pub/elgb/astorb.dat">here</a>. And if this
fails, try ftp'ing astorb.dat to yourself using the recipe below (except
type &quot;get astorb.dat&quot; rather than &quot;get astorb.dat.gz&quot;).
To name the file on a Netscape browser, click on &quot;File&quot;, then on
&quot;Save as&quot;, then on &quot;OK&quot; (the file will automatically be
named astorb.dat unless you choose another name at this point).
<br><br>
<li>If the above doesn't work or if you know someone who would like
astorb.dat and has ftp but not WWW access, note that the compressed version
is available via anonymous ftp at ftp.lowell.edu/pub/elgb/astorb.dat.gz, as
are text versions (astorb.txt and astorb_landmarks.txt) of astorb.html and
astorb_landmarks.html. Type the following commands:
<br><br>ftp ftp.lowell.edu
<br>Name: anonymous
<br>Password: <code>your email address</code>
<br>ftp&gt;cd pub/elgb
<br>ftp&gt;get astorb.txt
<br>ftp&gt;get landmarks.txt
<br>ftp&gt;get astorb.dat.gz
<br>ftp&gt;quit
<br><br>
astorb.dat.gz has been compressed using a public-domain utility called
<code>gzip</code>. To decompress the file (which will result in file
astorb.dat), type
<br>
gunzip astorb.dat.gz
<br><br>
<ul>
<li><code>gzip</code> code is available at
<a href="ftp://prep.ai.mit.edu/pub/gnu/gzip-1.2.4.tar">
prep.ai.mit.edu/pub/gnu/gzip-1.2.4.tar</a> (UNIX version) and
<a href="ftp://prep.ai.mit.edu/pub/gnu/gzip-1.2.4.msdos.exe">
prep.ai.mit.edu/pub/gnu/gzip-1.2.4.msdos.exe</a> (DOS version).
The <code>gzip</code> software accommodates both the <code>gzip</code>
and the <code>gunzip</code> commands.
<br><br>Type the following commands:
<br><br>ftp prep.ai.mit.edu
<br>Name: anonymous
<br>Password: <code>your email address</code>
<br>ftp&gt;cd pub/gnu
<br>ftp&gt;get gzip-1.2.3.tar  (or get gzip-1.2.4.msdos.exe)
<br>ftp&gt;quit
<br><br>
</ul>
<li>Tell your colleagues lacking both web and ftp access that we can supply
them with a compressed copy of the file along with the decompression software,
preferably on 3.5-in (9-cm) diskettes, in either UNIX or DOS format. To
arrange delivery, email us at
<a href="mailto:koehn@lowell.edu">koehn@lowell.edu </a> or call Bruce Koehn at
+1-520-774-3358 (fax +1-520-774-6296), specifying the medium and format you
prefer.
</ul>
    </p>
    <p>
      <font size = +1><b> Incremental update files</b></font>
      In response to users who have difficulty downloading the complete
      astorb.dat (see above for instructions), we have instituted (9 October
      1996) a method of logging daily changes in the orbital elements therein.
      Users will find files such as yymmdd.add and yymmdd.del in our public
      ftp area accessible from the WWW. These cover update activities for the
      past 30 days or more. Thus, 961007.add comprises records for asteroids
      whose orbital elements were either added to or replaced in astorb.dat on
      7 October 1996; and 960930.del contains records for asteroids whose
      orbits were deleted from astorb.dat on 30 September 1996. Note the
      following: (1) The *.add files are refreshed every day. Thus, an orbit
      that was replaced on, say, 961001 and then again on 961002 will be found
      only in the 961002.add file on or after the latter date. (2) The *.add
      files reflect changes in orbital elements only. Changes to other
      parameters (such as H, G, and integer codes), as well as daily updates
      of ephemeris uncertainties, are not reported in the *.add files. Users
      who are interested in the latter should download the entire astorb.dat.
      To download the *.add and *.del files, add the commands
      <br>
      <br>ftp&gt;mget *.add
      <br>ftp&gt;mget *.del
      <br>
      <br>to the ftp instructions above.
    </p>
    <p>
      <font size = +1><b>File Structure</b></font>
      Here are two sample records (with one line of parameter numbers
      above and three lines of column counts below):
    <pre>
(1)   (2)                (3)             (4)    (5)  (6)  (7)   (8)
    1 Ceres              E. Bowell        3.34  0.12 0.72 913.0 G?
 1693 Hertzsprung        E. Bowell       10.97  0.15 0.74  39.5 C
         0         0         0         0         0         0         0
         1         2         3         4         5         6         7
1234567890123456789012345678901234567890123456789012345678901234567890
 
  (9)                   (10) (11)  (12)     (13)       (14)       (15)
  0   0   0   0   0   0 56959 4750 19960427  80.477333  71.802404  80.
  0   0   0   0   0   0 20972   25 19960427 322.276332 234.698906  70.
         0         0         1         1         1         1         1
         8         9         0         1         2         3         4
1234567890123456789012345678901234567890123456789012345678901234567890
 
       (16)      (17)       (18)        (19)     (20)     (21)    (22)
659857 10.600303 0.07604100   2.76788714 19960414 2.3E-02  1.4E-04 199
393559 11.942428 0.27460300   2.79629204 19950513 9.0E-01  7.9E-03 199
         1         1         1         1         1         2         2
         5         6         7         8         9         0         1
1234567890123456789012345678901234567890123456789012345678901234567890
 
     (23)             (24)             (25)
60416 2.7E-02 19960530 3.1E-02 20040111 3.1E-02 20040111
60416 1.2E+00 19960610 1.3E+00 20010812 9.0E-01 20010813
         2         2         2         2         2
         2         3         4         5         6
12345678901234567890123456789012345678901234567890123456
    </pre>
    <p>
      A FORTRAN format statement for reading a record in astorb.dat is:
      <br><br>
      A5,1X,A18,1X,A15,1X,A5,1X,F5.2,1X,A4,1X,A5,1X,A4,
      1X,6I4,1X,<br>2I5,1X,I4,2I2.2,3(1X,F10.6),F10.6,1X,F10.8,
      1X,F12.8,1X,I4,2I2.2,1X,F7.2,1X,F8.2,1X,I4,2I2,3(1X,F7.2,1X,I4,2I2)
    </p>
    <p>
      Note that some numerical data (e.g., asteroid number) are encoded as
      character variables. You may need to decode them. Also note that
      the above format statement was updated on Monday 5 July 1999.
    </p>
    <p>
      Parameters are:
    </p>
      <table border>
        <tr>
          <th>Parameter</th>
          <th>Description</th>
        </tr>
        <tr>
          <td align="right">(1)</td>
          <td>Asteroid number (blank if unnumbered).</td>
        </tr>
        <tr>
          <td align="right">(2)</td>
          <td>Name or preliminary designation.</td>
        </tr>
        <tr>
          <td align="right">(3)</td>
          <td>Orbit computer.</td>
        </tr>
        <tr>
          <td align="right">(4)</td>
          <td>Absolute magnitude H, mag [see
          <cite>
            E. Bowell et al., pp. 549-554, in
             &quot;Asteroids II&quot;, R. P. Binzel et al. (eds.),
             The University of Arizona
             Press, Tucson, 1989
          </cite>and more recent<cite> Minor Planet Circulars</cite>].
             Note that H may be
             given to 2 decimal places
             (e.g., 13.41), 1 decimal place (13.4) or as an integer (13),
             depending on its estimated accuracy. H is given to two
             decimal places for all unnumbered asteroids, even though it
             may be very poorly known.</td>
        </tr>
        <tr>
          <td align="right">(5)</td>
          <td>Slope parameter G (
             <cite>ibid.</cite>).</td>
        </tr>
        <tr>
          <td align="right">(6)</td>
          <td>Color index B-V, mag (blank if unknown; see <cite>E. F. Tedesco,
             pp. 1090-1138, op. cit. </cite>).</td>
        </tr>
        <tr>
          <td align="right">(7)</td>
          <td>IRAS diameter, km (blank if unknown; taken from the Small
             Bodies Node of the Planetary Data System.</td>
        </tr>
        <tr>
          <td align="right">(8)</td>
          <td>IRAS Taxonomic classification (blank if unknown;
             <cite>ibid.</cite>).</td>
        </tr>
        <tr>
          <td align="right">(9)</td>
          <td>Six integer codes (see table of explanation below).
             Note that not all
             codes have been correctly computed.</td>
        </tr>
        <tr>
          <td align="right">(10)</td>
          <td>Orbital arc, days, spanned by observations used in orbit
             computation.</td>
        </tr>
        <tr>
          <td align="right">(11)</td>
          <td>Number of observations used in orbit computation.</td>
        </tr>
        <tr>
          <td align="right">(12)</td>
          <td>Epoch of osculation, yyyymmdd (TDT). The epoch is the
              Julian date ending
              in 00.5 nearest the date the file was created.
              Thus, as the file is updated, epochs will
              succeed each other at 100-day intervals on or after
              Julian dates ending in 50.5 (19980328, 19980706,
              19981014, 19990122,...)</td>
        </tr>
        <tr>
          <td align="right">(13)</td>
          <td>Mean anomaly, deg.</td>
        </tr>
        <tr>
          <td align="right">(14)</td>
          <td>Argument of perihelion, deg (J2000.0).</td>
        </tr>
        <tr>
          <td align="right">(15)</td>
          <td>Longitude of ascending node, deg (J2000.0).</td>
        </tr>
        <tr>
          <td align="right">(16)</td>
          <td>Inclination, deg (J2000.0).</td>
        </tr>
        <tr>
          <td align="right">(17)</td>
          <td>Eccentricity.</td>
        </tr>
        <tr>
          <td align="right">(18)</td>
          <td>Semimajor axis, AU.</td>
        </tr>
        <tr>
          <td align="right">(19)</td>
          <td>Date of orbit computation, yymmdd (MST, = UTC - 7 hr).</td>
        </tr>
        <tr>
          <td align="right">(20)</td>
          <td>Absolute value of the current 1-<img alt="sigma" align="bottom"
              src="http://www.lowell.edu/users/elgb/pics/sigma.gif"> ephemeris
              uncertainty (CEU), arcsec.</td>
        </tr>
        <tr>
          <td align="right">(21)</td>
          <td>Rate of change of CEU, arcsec/day.</td>
        </tr>
        <tr>
          <td align="right">(22)</td>
          <td>Date of CEU, yyyymmdd (0 hr UT).</td>
        </tr>
        <tr>
          <td align="right">(23)</td>
          <td>Next peak ephemeris uncertainty (PEU), arcsec, from date of CEU,
              and date of its occurrence, yyyymmdd.</td>
        </tr>
        <tr>
          <td align="right">(24)</td>
          <td>Greatest PEU, arcsec, in 10 years from date of CEU, and date of
              its occurrence, yyyymmdd.</td>
        </tr>
        <tr>
          <td align="right">(25)</td>
          <td>Greatest PEU, arcsec, in 10 years from date of next PEU, and
              date of its occurrence, yyyymmdd, if two observations (of
              accuracy equal to that of the observations currently included in
              the orbit--typically &#177 1 arcsec) were to be made on the date
              of the next PEU [parameter (23)].</td>
        </tr>
      </table>
<p>
  The meanings of the six integer codes [parameter (9)] are as follows
  (reference to &quot;type 6:7&quot;, for example, means code 6, value 7):
</p>
    <center>
      <table border>
        <tr>
          <th>Code</th><th>Value</th><th>Explanation</th>
        </tr>
        <tr>
          <td align="right">1</td>
          <td></td>
          <td align="center">
            Planet-crossing asteroids.
            <br>
            <i>
              Note: Because some orbits are very poor (or erroneously linked),
              there may be errors in assignment of these parameter values.
            </i>
          </td>
        </tr>
        <tr>
          <td rowspan=6></td>
          <td align="right">1</td>
          <td>
Aten asteroids (a&nbsp;&lt;&nbsp;1.0 AU).
          </td>
        </tr>
        <tr>
          <td align="right">2</td>
          <td>
Apollo asteroids (a&nbsp;&gt;&nbsp;1.0 AU; 0&nbsp;&lt;&nbsp;q&nbsp;&lt;&nbsp;1.0
          </td>
        </tr>
        <tr>
          <td align="right">4</td>
          <td>
Amor asteroids (a&nbsp;&gt;&nbsp;1.0167 AU; 1.0167&nbsp;&lt;&nbsp;q&nbsp;&lt;&nb
          </td>
        </tr>
        <tr>
          <td align="right">8</td>
          <td>
Mars crossers (1.3&nbsp;&lt;&nbsp;q&nbsp;&lt;&nbsp;1.6660 AU).</td>
        </tr>
        <tr>
          <td align="right">16</td>
          <td>
Outer-planet crossers (excluding Jupiter and Mars Trojans). Asteroids that cross
or pass into the heliocentric distance zones between the perihelion and aphelion
distances of Jupiter (4.950 to 5.455 AU), Saturn (9.009 to 10.069 AU),
Uranus (18.274 to 20 089 AU), and/or Neptune (29.800 to 30.317 AU).
          </td>
        </tr>
        <tr>
          <td align="right">n</td>
          <td>
 
Asteroids (excluding Mars and Jupiter Trojans) that cross both inner-
and outer-planet orbits. For example, an asteroid having n&nbsp;=&nbsp;24 crosse
the orbits of both Mars (q&nbsp;&lt;&nbsp;1.6660 AU) and Jupiter
(Q&nbsp;>&nbsp;4.950 AU).
          </td>
        </tr>
        <tr>
          <td align="right">2</td>
          <td></td>
          <td align="center">Orbit computation.</td>
        </tr>
        <tr>
          <td rowspan=6></td>
          <td align="right">1</td>
          <td>
Orbits derived from uncertainly, perhaps erroneously linked
observations.
          </td>
        </tr>
        <tr>
          <td align="right">2</td>
          <td> Eccentricity assumed.</td>
        </tr>
        <tr>
          <td align="right">4</td>
          <td> Eccentricity and semimajor axis assumed.</td>
        </tr>
        <tr>
          <td align="right">8</td>
          <td>
Mainly for numbered asteroids, omitted observations have resulted in
degradation of a so-called orbit-quality parameter (OQP, see
<cite>K. Muinonen and E. Bowell, Icarus 104, 255-279, 1993</cite>),
generally by more than 0.1.  The corresponding ephemeris uncertainty
has increased by about 25% or more.
          </td>
        </tr>
        <tr>
          <td align="right">16</td>
          <td>
          OQP degrades by more than 0.1 if unsubstantiated observations
          (e.g., one-night apparitions) are omitted.</td>
        </tr>
        <tr>
          <td align="right">32</td>
          <td>
Orbit derived from data containing observations not in Minor Planet Center
files.
          </td>
        </tr>
        <tr>
          <td></td>
          <td align="right">64</td>
          <td>
H is unknown. H = 14 mag assumed.
          </td>
        </tr>
        <tr>
          <td></td>
          <td align="right">128</td>
          <td>
Asteroid sought, but not found.
          </td>
        </tr>
        <tr>
          <td></td>
          <td align="right">n</td>
          <td>
          Sum of preceding entries. For example, n&nbsp;=&nbsp;3 pertains to an
          uncertainly linked orbit for which the eccentricity was assumed.</td>
        </tr>
        <tr>
          <td align="right">3</td>
          <td></td>
          <td align="center">
          Asteroids observed during the course of major surveys. Our definition
          includes asteroids that were observed but not discovered during the
          course of a survey.</td>
        </tr>
        <tr>
          <td rowspan=6></td>
          <td align="right">1</td>
          <td> Palomar-Leiden survey (PLS) asteroids. </td>
        </tr>
        <tr>
          <td align="right">2</td>
          <td> Palomar-Leiden T-2 survey asteroids.</td>
        </tr>
        <tr>
          <td align="right">4</td>
          <td> Palomar-Leiden T-3 survey asteroids.</td>
        </tr>
        <tr>
          <td align="right">8</td>
          <td>
          U.K. Schmidt Telescope-Caltech asteroid survey (UCAS)
          asteroids.</td>
        </tr>
        <tr>
          <td align="right">16</td>
          <td> Palomar-Leiden T-1 survey asteroids.</td>
        </tr>
        <tr>
          <td align="right">n</td>
          <td>
          Asteroids observed in more than one survey. For example,
          n&nbsp;=&nbsp;3
          denotes an asteroid observed in both the PLS and T-2 surveys.</td>
        </tr>
        <tr>
          <td align="right">4</td>
          <td></td>
          <td align="center">
          Minor Planet Center (MPC) critical-list numbered asteroids.
          </td>
        </tr>
        <tr>
          <td rowspan=7></td>
          <td align="right">1</td>
          <td> Lost asteroid.</td>
        </tr>
        <tr>
          <td align="right">2</td>
          <td> Asteroids observed at only two apparitions.</td>
        </tr>
        <tr>
          <td align="right">3</td>
          <td> Asteroids observed at only three apparitions.</td>
        </tr>
        <tr>
          <td align="right">4</td>
          <td>
          Asteroids observed at four or more apparitions, last more than
          ten years ago.</td>
        </tr>
        <tr>
          <td align="right">5</td>
          <td>
          Asteroids observed at four or more apparitions, only one night
          in last ten years.</td>
        </tr>
        <tr>
          <td align="right">6</td>
          <td>
          Other poorly observed asteroids observed at four or more
          apparitions.</td>
        </tr>
        <tr>
          <td align="right">7</td>
          <td> Absolute magnitude poorly known (not on MPC critical-list).</td>
        </tr>
        <tr>
          <td align="right">5</td>
          <td></td>
          <td align="center">
            Lowell Observatory and related discoveries
          </td>
        </tr>
        <tr>
          <td rowspan=2></td>
          <td align="right">1</td>
          <td> Asteroids discovered by E. Bowell.</td>
        </tr>
        <tr>
          <td align="right">2</td>
          <td> Non-Bowell discoveries from Lowell search programs.</td>
        </tr>
        <tr>
          <td></td>
          <td align="right">3</td>
          <td>
          Sum of preceding entries. n&nbsp;=&nbsp;3 pertains to an asteroid
          discovered jointly by E. Bowell and another person connected with
          Lowell search programs.</td>
        </tr>
        <tr>
          <td align="right">6</td>
          <td></td>
          <td align="center">
          Rank, in decreasing importance, for our collaborative program of
          astrometry using the transit circle of the U.S. Naval Observatory
          Flagstaff Station.</td>
        </tr>
        <tr>
          <td rowspan=7></td>
          <td align="right">10</td>
          <td>
          Exceptionally important, to be observed frequently. Principally
          space mission targets and occultation candidates.</td>
        </tr>
        <tr>
          <td align="right">9</td>
          <td> Asteroids useful for mass determination.</td>
        </tr>
        <tr>
          <td align="right">8</td>
          <td>
          Asteroids for which one or two additional nights' observation
          are required to satisfy orbit-update requirements.
          Asteroids of type 6:7 whose ephemeris uncertainties are between
          2 and 5 arcsec within the next ten years or so.</td>
        </tr>
        <tr>
          <td align="right">7</td>
          <td>
Bowell unnumbered discoveries whose ephemeris uncertainties are less
than 2 arcsec within the next ten years or so.  MPC critical-list
asteroids.
          </td>
        </tr>
        <tr>
          <td align="right">6</td>
          <td> Planet-crossers of type 6:5.</td>
        </tr>
        <tr>
          <td align="right">5</td>
          <td>
          Numbered asteroids whose ephemeris uncertainties are between
          2 and 5 arcsec within the next ten years or so.
          Unnumbered asteroids that should be numberable after one or two
          more nights' observation.</td>
        </tr>
    </table>
      </center>
    <p>
Note that the codes have not been carefully checked. There are doubtless
many errors.
    </p>
      <font size = +1><b> Notes on File Content</b></font>
<p>
<li>Osculating elements [parameters (13) through (18)] are heliocentric.
</p>
<p>
<li>It may be assumed that ephemeris uncertainties are along the line of
variation. Except for very accurately known orbits (ephemeris uncertainty
< 1 arcsec) and very poorly known orbits (arc < 10 days), positional
uncertainty perpendicular to the line of variation is usually very small
compared to that along the line of variation.
</p>
<p>
<li>The current ephemeris uncertainty [CEU, parameter (20)] and its rate of
change [parameter (21)] indicate whether an asteroid ought to be located in an
observer's field of view. A CEU greater than all three of the peak ephemeris
uncertainties [PEUs, parameters (23) through (25)] implies that the asteroid's
ephemeris uncertainty is currently greater than at any time in the next ten
years. Such asteroids are prime targets for observation because their orbits
are subject to the greatest improvement for years to come. Note that, because
ephemeris uncertainties have been computed using 2-body rather than n-body
error propagation (see <cite>K. Muinonen and E. Bowell, Icarus <b>104</b>,
255-279, 1993</cite>), uncertainties for Earth-approaching asteroids may have
been misestimated by a factor of several.
</p>
<p>
<li>Most single-apparition asteroids are hopelessly lost. They have large
CEUs--typically &#177 10<sup>5</sup> to &#177 10<sup>6</sup> arcsec. CEUs may
have been imperfectly computed for such asteroids (though it should hardly
matter) because of poorly known or unknown observational accuracy and/or
because orbital eccentricities have been assumed (integer code 2 equals 2 or
4; see the integer-code table above). Users who wish to estimate ephemeris
uncertainties for lost asteroids at times close to when they were observed may
make use of the approximate formulae (formulae require Netscape Version 2.0 or
higher for proper rendering):
    </p>
    <center>
      <p>
<img alt="sigma" align="bottom" src=
"http://www.lowell.edu/users/elgb/pics/sigma.gif">(t) = &#177;4500(q -
1) (t<sub>f</sub> - t) / [t<sub>arc</sub><sup>2</sup> (N - 3)<sup>1/2</sup>
<img alt="Delta" align="bottom" src=
"http://www.lowell.edu/users/elgb/pics/Delta.gif">] arcsec
<br>
<img alt="sigma" align="bottom" src=
"http://www.lowell.edu/users/elgb/pics/sigma.gif">(t) = &#177;4500(q -
1) (t - t<sub>l</sub>) / [t<sub>arc</sub><sup>2</sup> (N - 3)<sup>1/2</sup>
<img alt="Delta" align="bottom" src=
"http://www.lowell.edu/users/elgb/pics/Delta.gif">] arcsec,
      </p>
    </center>
    <p>
derived from <cite>K. Muinonen, E. Bowell, and L. H. Wasserman (Planet. Space
Sci. <b>42</b>, 307-313, 1994</cite>). Here, <img alt="sigma" align="bottom"
src="http://www.lowell.edu/users/elgb/pics/sigma.gif">(t) is the 1-<img
alt="sigma" align="bottom" src=
"http://www.lowell.edu/users/elgb/pics/sigma.gif"> sky-plane
uncertainty, along the line of variation, at time t; q is the
perihelion distance in AU; t<sub>f</sub> and t<sub>l</sub> are the times of
the first and last observations, respectively (t<sub>f</sub> - t and
t - t<sub>l</sub> are in days); t<sub>arc</sub> and N are parameters (10) and
(11) above; and <img alt="Delta" align="bottom"
src= "http://www.lowell.edu/users/elgb/pics/Delta.gif"> is the Earth-asteroid
distance in AU. For long-unobserved asteroids, t<sub>f</sub> and t<sub>l</sub>
may be approximated from the designation. Thus, for 1982 EE, which has a 9-day
arc, t<sub>f</sub> may be taken as 1 March 1982 and t<sub>l</sub> as 15 March
1982. The formula should be accurate to within a factor of five.
</p>
<p>
<li>Peak ephemeris uncertaities [parameters (23) through (25)] generally occur
near opposition or conjunction (the latter are more prevalent for
Earth-crossing asteroids). The next PEU [parameter (23)] usually indicates the
best time to make astrometric observations for orbit improvement, as will the
PEU over the next 10 years [parameter (24)]. Special effort should be made to
observe asteroids whose next PEUs are the greatest during the next 10 years
[i.e., parameter (23) exceeds both parameters (24) and (25)]. Parameter (25)
may be used to quantify the amount of orbital improvement that would result
from observing at or near the date of next PEU. For example, if the next PEU
is 1.2D+02 arcsec, and parameter (25) has value 6.0D+00 arcsec, a 20-fold
ephemeris improvement (and approximately equal improvement in the
unceratinties of the orbital elements) could be made. Note that numbered
asteroids whose orbits are satisfactory have all three PEUs less than about
&#177 2 arcsec (absolute). Consequently, numbered asteroids whose ephemeris
uncertainties, as indicated by the CEU and PEUs, at any time exceed about
2 arcsec should be targeted for observation. Unnumbered asteroids whose
ephemeris uncertainties [as per parameter (25)] could be brought below about
&#177 2 arcsec, would probably then be candidates for numbering. A parameter
(25) PEU greater than a parameter (24) PEU implies that observing at or near
the date of the next PEU [parameter (23)] may actually cause ephemeris and
orbit degradation. Thus, there is no point in making such observations unless
they are numerous and/or of high accuracy.
</li>
    </p>
    <p>
      <font size = +1><b> Computational Details</b></font>
To produce the database,
our variable-timestep differential orbit correction program was run in
an automatic mode.  Perturbation due to all major planets (Mercury
through Pluto, Earth and Moon separately), Ceres (assumed mass
5.0&#215;10<sup>-10</sup> M<img alt="_Sun" align="center" src=
"http://www.lowell.edu/users/elgb/pics/smsun.gif">), Pallas
(1.1&#215;10<sup>-10</sup> M<img alt="_Sun" align="center" src=
"http://www.lowell.edu/users/elgb/pics/smsun.gif">), and Vesta
(1.4&#215;10<sup>-10</sup> M<img alt="_Sun" align="center" src=
"http://www.lowell.edu/users/elgb/pics/smsun.gif">)
were included. Planetary positions were derived from JPL's DE403 planetary
ephemeris. Positions of the three perturbing asteroids were derived, by
iteration, from our own orbits. Relativistic effects have not been included.
The orbit of one numbered asteroid (1566 Icarus) is known to be imperfect as
it requires inclusion of relativistic effects. The orbits of other
close-Sun-approaching asteroids are doubtless similarly affected, but their
observational (O-C) residuals appear to be satisfactory.
    </p>
    <p>
For numbered asteroids, we have adopted a uniform policy regarding the
inclusion or exclusion of observations in the orbit determination:
namely, to exclude observations whose great-circle sky-plane residuals
exceed 2.3 arcsec. (We have found from experience that, for
well-determined orbits, 2.3 arcsec is an appropriate residual
threshold separating &quot;good&quot; and &quot;bad&quot;
observations.) For numbered asteroids of type 2:8 in the integer-code
table above, our policy has resulted in degradation of the
orbit-quality parameter (OQP), which is a reliable (logarithmic)
measure of an asteroid orbit's quality, and which (for non-Earth
approachers) correlates well with ephemeris uncertainty. Such
asteroids need orbit improvement to the point where the exclusion of
&quot;poor&quot; observations no longer degrades the OQP. For
unnumbered asteroids, we have retained obviously inferior observations
where doing so improved the OQP and ephemeris uncertainty, thus making
it easier to reobserve them; these asteroids are identified by integer code
2:16.
    <p>
      <font size = +1><b> Upcoming Changes in astorb.dat</b></font>
Eventually, we intend to produce a version of the database in a format
resembling that espoused in our ACM93 paper [E. Bowell, K. Muinonen, and L. H.
Wasserman (1994). A public-domain asteroid orbit database. In <cite>
&quot;Asteroids, Comets, Meteors 1993&quot; (A. Milani et al., eds.), pp.
477-481. Kluwer, Dordrecht</cite>]. We will not be making this expanded file
publicly accessible until we have checked it fairly thoroughly, incorporated
it into our suite of asteroid-orbit software, and extracted data for a paper
entitled something like <cite>&quot;Orbit and ephemeris accuracy of
multi-apparition asteroids&quot;</cite>.
    </p>
    <p>
In addition, we are near to making a second run on orbits for numbered
asteroids in which close asteroid-asteroid encounters will be noted
and a new perturbation scheme that includes two or three dozen
asteroid perturbers is implemented.
    </p>
    <p>
We are also looking into the possibility of allowing approved WWW users to run
selected programs on our system (ephemerides; which asteroids are in a
given region of sky at a given time; selecting subsets of asteroids by
orbital elements, predicted magnitude, location in the sky, etc.).
    </p>
    <p>
      <font size = +1><b>Acknowledgment and Attribution</b></font>
The research and computing needed to generate astorb.dat were funded
principally by NASA grant NAG5-4741, and in part by the Lowell Observatory
endowment. astorb.dat may be freely used, copied, and transmitted provided
attribution to Dr. Edward Bowell and the aforementioned funding sources is
made. Hypertext links to this WWW site are welcome.
    </p>
    <p>
Ted Bowell
    </p>
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     <h5>
       <i>
        Last updated 20 Jan 2000 at 19:10:37 U.T.
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         Contact: Bruce Koehn
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         </a>
         <br>
         Web Curators: 
         <a href="http://www.lowell.edu/users/elgb/bowell.html">
           Ted Bowell
         </a>
         and
         <a href="http://www.lowell.edu/users/koehn/koehn.html">
           Bruce Koehn
         </a>
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